Cooper-pair box (charge) qubit

Description

A nanometre-scale superconducting electrode connected to a reservoir via a Josephson junction constitutes an artificial two-level electronic system: a single-Cooper-pair box. The two levels consist of charge states (differing by 2e, where e is the electronic charge) that are coupled by tunnelling of Cooper pairs through the junction. Although the two-level system is macroscopic, containing a large number of electrons, the two charge states can be coherently superposed. The Cooper-pair box has therefore been suggested as a candidate for a quantum bit or ‘qubit’—the basic component of a quantum computer.

Figure

Motivation

The original “artificial atom” formed in a superconducting circuit. Because of its sensitivity to charge noise, alternative qubit approaches that offer some immunity to charge noise were sought after.

References

• https://www.nature.com/articles/19718
• https://iopscience.iop.org/article/10.1238/Physica.Topical.076a00165/pdf
• https://iopscience.iop.org/article/10.1088/1367-2630/7/1/180

Linked Papers

• nakamura-1999-cpb-coherent-oscillation

Related Entries

• phase-qubit
• flux-qubit

Seed Metadata

• date_published: 1999-04-29

Physics

The Cooper pair box Hamiltonian:

$H=4E_C(\hat{n}-n_g{)}^2-E_J\cos \hat{\phi }$

Operating in the charge regime $E_C>E_J$, the qubit states are charge states $|n⟩$ and $|n+1⟩$ differing by one Cooper pair. At the charge degeneracy point $n_g=1/2$, the two lowest states are split by $E_J$. Gate voltage tunes $n_g=C_g{V}_g/2e$, controlling the qubit transition frequency. Highly sensitive to charge noise $\delta n_g$ at generic operating points.

Related Qubits

• transmon — descendant operating in $E_J\gg E_C$ for charge noise immunity
• fluxonium — inductive shunt alternative
• blochnium — quasicharge regime

Key Metrics

Metric	Value	Notes	Fidelity reference
Qubit coherence $T_1$	~1–10 μs	Limited by charge noise	Nakamura et al. 1999
Qubit coherence $T_2$	~0.5–5 μs	At sweet spot ($n_g=1/2$)	Vion et al. 2002
Gate fidelity (1Q)	~99%	Voltage-pulse driven	Vion et al. 2002
Gate fidelity (2Q)	~95%	Capacitive coupling	Yamamoto et al. 2003
Gate time (1Q)	~1–10 ns	Fast voltage pulses	—
Gate time (2Q)	~10–50 ns		—
Readout fidelity	~90–95%	Probe junction or SET	Vion et al. 2002
Qubit footprint	~1 × 1 μm²	Very compact	—
Operating temperature	20–50 mK	Dilution refrigerator	—
Connectivity	Fixed capacitive	Nearest-neighbor	—